{"id":935,"date":"2014-02-17T15:46:45","date_gmt":"2014-02-17T20:46:45","guid":{"rendered":"https:\/\/my.dev.vanderbilt.edu\/mcml\/?page_id=935"},"modified":"2014-02-17T15:46:45","modified_gmt":"2014-02-17T20:46:45","slug":"multiscale-modeling-of-random-nano-and-micro-fiber-reinforced-cementitious-composites-2","status":"publish","type":"page","link":"https:\/\/my.dev.vanderbilt.edu\/mcml\/cv\/multiscale-modeling-of-random-nano-and-micro-fiber-reinforced-cementitious-composites-2\/","title":{"rendered":"Multiscale Modeling of Random Nano- and Micro-Fiber Reinforced Cementitious Composites"},"content":{"rendered":"

Research Sponsor: <\/span><\/h4>\n
  • Vanderbilt University Grant Research Program <\/span><\/li>\n
  • Vanderbilt University Institute for Software Integrated Systems (ISIS) <\/span><\/li>\n

    Investigators: <\/span><\/h4>\n

    Matthew G. Pike and Caglar Oskay <\/span>
    \n<\/p>\n

    Research Goals and Methods<\/h2>\n

    Goals:<\/span><\/h4>\n
  • To gain a fundamental understanding of the interactions between the fibers and the cement matrix in carbon nano- and micro-fiber reinforced cement composites<\/span><\/li>\n
  • To evaluate the effects of the chemical structure of the interface on the macroscopic mechanical failure properties<\/span><\/li>\n

    Multiscale Computational Framework:<\/span><\/h4>\n
  • Composite response controlled at the molecular scale through the chemical and mechanical interactions<\/span><\/li>\n
  • Nanoscale investigations and nanoscopically informed embedded cohesive law<\/span><\/li>\n
  • Link the material microstructure to the composite mesoscale: based on the overall response of the RVE<\/span><\/li>\n

    Computational Design of Carbon Nano- and Micro-Fiber Reinforced Cementitious Composites:<\/span><\/h4>\n
  • Random short fiber reinforced composite material<\/span><\/li>\n
  • The inter-facial interaction between the matrix and the reinforcement has significant effect on the overall response of the composite structure<\/span><\/li>\n
  • Use of the extended finite element method (X-FEM)to model the fibers in the matrix<\/span><\/li>\n


    \n\"\"<\/a>
    \n<\/p>\n

    Modeling Short Fibers Reinforced Composites Using XFEM<\/h2>\n

    Representative Volume Element (RVE):<\/span><\/h4>\n
  • Constitutive response of the cohesive zone model for interdependent damage-plasticity modeling of the cement phase<\/span><\/li>\n
  • Random short-fiber reinforced matrix idealization<\/span><\/li>\n
  • XFEM framework to evaluate the response of the RVE<\/span><\/li>\n

    Extended Finite Element Method (XFEM):<\/span><\/h4>\n
  • Fibers accounted for by using additional enrichment functions <\/span><\/li>\n
  • Enrichment of the finite element approximation by additional functions that model the internal boundaries<\/span><\/li>\n
  • Fibers can be modeled as rigid or flexible<\/span><\/li>\n


    \n\"\"<\/a><\/p>\n

  • Complex finite element discretizations that require resolution of fibers are eliminated<\/span><\/li>\n
  • N(x<\/strong>): nodal enrichment function, u\u0302<\/strong>: nodal value, \u03c8(x<\/strong>): enrichment function, c\u0302<\/strong>: additional degree of freedom nodal value<\/span><\/li>\n


    \n\"\"XFEM Element Types<\/span><\/a><\/p>\n

    Nodal Enrichment Function:<\/span><\/h4>\n
  • Enrichment function of fiber inclusion comprised of level set functions<\/span><\/li>\n
  • Level set functions for fiber interface and fiber tips separately<\/span><\/li>\n


    \n\"\"<\/a><\/p>\n

  • \u03a6\u03b1<\/sub>(x<\/strong>)=(x<\/strong>–x<\/strong>i<\/sub>)\u00b7t<\/strong> : level set function at fiber tip, i – tracks the motion of each fiber tip<\/span><\/li>\n
  • \u03a6c<\/sub>(x<\/strong>)=min ||x<\/strong>–x<\/strong>r<\/sub>|| : level set function at interface – tracks the motion of the fiber interface<\/span><\/li>\n


    \n\"\"Enrichment Function<\/span><\/a>
    \n
    \n\"\"Enriched Nodal Basis Functions<\/span><\/a>
    \n<\/p>\n

    Fiber Response<\/h2>\n

    Rigid Fibers:<\/span><\/h4>\n
  • Assume each fiber moves as a rigid body as does not deform<\/span><\/li>\n
  • Described through rotation and translation<\/span><\/li>\n
  • Penalty method applied to fiber constraint at fiber\/matrix interface<\/span><\/li>\n


    \n\"\"<\/a><\/p>\n

    Flexible Fibers:<\/span><\/h4>\n
  • Assume each fiber is flexible and do not bend but stretch under loading<\/span><\/li>\n
  • Flexibility of fiber decrease the strength of the matrix<\/span><\/li>\n
  • The energy from the stretch is added to the system<\/span><\/li>\n


    \n\"\"<\/a>
    \n<\/p>\n

    Fiber De-Bonding and Cohesive Embedded Laws<\/h2>\n

    Fiber De-Bonding:<\/span><\/h4>\n
  • Fibers will de-bond from the matrix once the loading reaches a critical stress<\/span><\/li>\n
  • Additional term added to discretization at account for the de-bonding:<\/span><\/li>\n


    \n\"\"<\/a>
    \n
    \n\"\"<\/a>
    \n
    \n\"\"De-Bonding Enrichment Function<\/span><\/a><\/p>\n

    Cohesive Embedded Law:<\/span><\/h4>\n
  • Energy based, nanoscopically informed cohesive embedded law<\/span><\/li>\n
  • Separation over the interface of the fiber and matrix, resisted by cohesive tractions<\/span><\/li>\n
  • Non linear constitutive relationship between cohesive tractions and the displacement jumps along the fiber cement interface as a function of the molecular structure<\/span><\/li>\n


    \n\"\"Cohesive Traction relationship and Fiber De-Bonding Motion<\/span><\/a>
    \n<\/p>\n

    Summary<\/h2>\n

    Multiscale Computational Framework for Modeling the Mechanical Response of Nano- and Micro-Fiber Reinforced Cementitious Composites:<\/span><\/h4>\n
  • An efficient XFEM approach is proposed to evaluate the RVE response<\/span><\/li>\n
  • Nano- and micro-fibers modeled for rigid, flexibility and de-bonding of fibers<\/span><\/li>\n
  • Nanoscale response with the nanoscopically informed cohesive embedded law<\/span><\/li>\n

    Future Potential:<\/span><\/h4>\n
  • Pathway to achieve simulation based molecular scale engineering of cementitious composites<\/span><\/li>\n
  • Aid in the composite material design process<\/span><\/li>\n","protected":false},"excerpt":{"rendered":"

    Research Sponsor: Vanderbilt University Grant Research Program Vanderbilt University Institute for Software Integrated Systems (ISIS) Investigators: Matthew G. Pike and Caglar Oskay Research Goals and Methods Goals: To gain a fundamental understanding of the interactions between the fibers and the cement matrix in carbon nano- and micro-fiber reinforced cement composites To evaluate the effects of…<\/p>\n","protected":false},"author":235,"featured_media":0,"parent":5,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[],"class_list":["post-935","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/my.dev.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/pages\/935","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/my.dev.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/my.dev.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/my.dev.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/users\/235"}],"replies":[{"embeddable":true,"href":"https:\/\/my.dev.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/comments?post=935"}],"version-history":[{"count":114,"href":"https:\/\/my.dev.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/pages\/935\/revisions"}],"predecessor-version":[{"id":1067,"href":"https:\/\/my.dev.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/pages\/935\/revisions\/1067"}],"up":[{"embeddable":true,"href":"https:\/\/my.dev.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/pages\/5"}],"wp:attachment":[{"href":"https:\/\/my.dev.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/media?parent=935"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/my.dev.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/tags?post=935"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}